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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 6 — Mar. 12, 2012
  • pp: 6472–6477
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Teardrop-shaped surface-plasmon resonators

Majid Rasouli Disfani, Mohammad Sadegh Abrishamian, and Pierre Berini  »View Author Affiliations


Optics Express, Vol. 20, Issue 6, pp. 6472-6477 (2012)
http://dx.doi.org/10.1364/OE.20.006472


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Abstract

A new surface plasmon resonator, in the form of a metal cylinder shaped like a teardrop, is proposed and modeled using hypersingular integral equations. Illuminating the apex of the teardrop along its axis of symmetry with TM-polarised light excites equal-magnitude surface plasmons counter-propagating around its periphery. Interference of these counter-propagating surface plasmons leads to resonant modes having very sharp line-widths (~0.6 nm) and large quality factors (~3400). In water, a Au teardrop supports resonant modes having large bulk sensitivities (~1900 nm/RIU) and remarkably large figures-of-merit (~1700), about 1000 × larger than the figure-of-merit of, e.g., isolated Au nano-spheres. The scattering cross-section of the structure near resonant modes exhibits a Fano-like line-shape. The teardrop should find applications as a high-quality surface plasmon resonator or as a biosensing element.

© 2012 OSA

1. Introduction

Metal nano-particles (NPs) [1

1. C. R. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

, 2

2. M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photon. Rev. 2(3), 136–159 (2008). [CrossRef]

] are of considerable interest due to their ability to support strongly confined surface plasmon-polariton (SPP) resonances. They have found numerous applications, particularly to biosensors [3

3. M. Piliarik, P. Kvasnička, N. Galler, J. R. Krenn, and J. Homola, “Local refractive index sensitivity of plasmonic nanoparticles,” Opt. Express 19(10), 9213–9220 (2011). [CrossRef] [PubMed]

, 4

4. H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24(10), 5233–5237 (2008). [CrossRef] [PubMed]

]. Various metal geometries, ranging from curved-surface structures like disks [5

5. N. Large, J. Aizpurua, V. K. Lin, S. L. Teo, R. Marty, S. Tripathy, and A. Mlayah, “Plasmonic properties of gold ring-disk nano-resonators: fine shape details matter,” Opt. Express 19(6), 5587–5595 (2011). [CrossRef] [PubMed]

] and cylinders [6

6. H. Y. She, L. W. Li, O. J. Martin, and J. R. Mosig, “Surface polaritons of small coated cylinders illuminated by normal incident TM and TE plane waves,” Opt. Express 16(2), 1007–1019 (2008). [CrossRef] [PubMed]

], to sharp-angled structures like cubes [7

7. L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5(10), 2034–2038 (2005). [CrossRef] [PubMed]

] and wedges [8

8. E. Verhagen, L. K. Kuipers, and A. Polman, “Plasmonic nanofocusing in a dielectric wedge,” Nano Lett. 10(9), 3665–3669 (2010). [CrossRef] [PubMed]

], have been investigated. SPP resonances on such structures depend strongly on their shape, size and composition, and on the surrounding medium. Fano resonances involving SPPs in metal nano-structures have recently been observed [9

9. F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano 3(3), 643–652 (2009). [CrossRef] [PubMed]

13

13. A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B 70(12), 125113 (2004). [CrossRef]

]. In general, such resonances arise from the coupling of a narrow discrete resonance with a broad one [12

12. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

]. SPP Fano resonances are strongly dispersive and they are sharp so they have a high quality factor (Q) [9

9. F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano 3(3), 643–652 (2009). [CrossRef] [PubMed]

12

12. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

], and thus are also of strong interest for applications.

In this paper we propose a new surface plasmon resonator, in the form of a metal cylinder shaped like a teardrop, as sketched in Fig. 1
Fig. 1 Cross-section of a metal teardrop-shaped cylindrical resonator (εm) surrounded by dielectric (εd), illuminated by a TM-polarised plane wave at ϕinc.
. The structure is invariant along z (out of the page) and obtained from a wedge of angle β by closing its two flat surfaces of length a with a circular surface of radius r = a × tan(β/2). The normal to the circular surface coincides with the normal of the two flat surfaces at their ends. The permittivity of the metal is denoted εm and that of the dielectric background by εd.

The resonator is assumed illuminated by a transverse-magnetic (TM) polarised plane wave of magnitude E0 in the plane of incidence perpendicular to the z axis, at an angle of incidence ϕinc = 90°; the source is thus an x-polarised plane wave incident on the apex. The apex is taken as being perfectly sharp, although in practice a rounded apex of radius ~10 nm would behave similarly as far as the resonant modes are concerned.

Illuminating the teardrop directly onto its apex generates single-interface SPPs of equal magnitude that propagate along the flat surfaces, as sketched in Fig. 1 (the apex acts as a free-space to SPP coupler). The SPPs then propagate in opposite directions around the curved section (possibly with radiation), and back to the apex. Resonant modes are thus formed by the interference of oppositely propagating SPPs propagating along the teardrop perimeter.

2. Analysis in vacuum

The teardrop (εm) is assumed formed of Au [14

14. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

] and, initially, surrounded by vacuum (εd = ε0). The geometry is set to β = 30° and a = 1 μm, yielding r = 268 nm. We arrived at these dimensions via trials to produce resonant modes within the free-space wavelength range of λ0 = 600 to 2400 nm (altering the perimeter alters the resonant wavelengths). We investigate the scattering and resonant properties of this structure using single hypersingular integral equations (HIEs) [15

15. E. Marx, “Electromagnetic scattering from a dielectric wedge and the single hypersingular integral equation,” IEEE Trans. Antenn. Propag. 41(8), 1001–1008 (1993). [CrossRef]

] (the teardrop shape is inspired from [15

15. E. Marx, “Electromagnetic scattering from a dielectric wedge and the single hypersingular integral equation,” IEEE Trans. Antenn. Propag. 41(8), 1001–1008 (1993). [CrossRef]

]). HIEs can model accurately electromagnetic fields to distances as small as ~10−4λ0 from the structure, including the apex.

Figure 2
Fig. 2 Scattering cross-section of a Au teardrop in vacuum (thick red curve) and water (thin blue curve); the latter was multiplied by 0.5 before plotting.
shows the scattering cross-section of the teardrop bounded by vacuum (thick red curve), computed over the range of interest, as [1

1. C. R. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

]:
Cscat(λ0)=R|Escat(λ0)|2/|Einc(λ0)|2dδ
(1)
where R = 60 µm is the radius of the circle on which the electric field is sampled (far from the structure), is the elemental angle, and |Escat(λ0)| and |Einc(λ0)| are the scattered and incident electric field magnitudes at λ0, respectively. From Fig. 2, the structure is observed to resonate at four wavelengths (sharp peaks) with the longest resonant wavelength belonging to the lowest order resonance. It is noted that the resonances are asymmetric, especially at high-order, with line-shapes characteristic of Fano resonances [12

12. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

].

Table 1

Table 1. Scattering Cross-Section Parameters of Resonant Modes; Au Teardrop in Vacuum

table-icon
View This Table
| View All Tables
lists the resonant free-space wavelength λr, full-width at half-maximum (FWHM) and quality factor (Q) of the resonant modes (Q ~λr /FWHM which holds at high Q). The FWHM increases and the Q decreases as the mode order increases. This is consistent with the increasing attenuation of SPPs as λr decreases (with mode order). The highest Q of 3400 is observed for the first resonance (mode 1), which also has the narrowest FWHM of 0.60 nm.

Figure 3
Fig. 3 Distribution of |Escat| and of its y-component |Eyscat| normalised to E0, plotted on log and linear scales, for modes 1 (a-d) and 2 (e-h) of Table 1.
shows the distribution of |Escat| and of its y-component |Eyscat|, both normalised to E0 and plotted on log and linear scales, for mode 1 (top row) and mode 2 (bottom row). The log plots (left) illustrate the rapid field decay in the metal, characteristic of SPPs. The electric field of mode 1 is localised around the curved section of the teardrop (Fig. 3(d)), while for mode 2 the field is distributed around the curved section and the two flat surfaces (Fig. 3(h)).

The scattered x-directed electric field component |Exscat| (not shown) is distributed similarly to |Escat|. A different number of extrema was observed in the field distribution of all modes of Table 1 (cf. Figures 3(d) and 3(h)). Given the x-polarized excitation and the symmetry of the teardrop about the y-axis, |Eyscat| = 0 along this axis for all modes. There is no field localisation near the apex and negligible field enhancement throughout. Other resonant modes may exist and may be revealed for a non-symmetric excitation (i.e., for excitation at other angles of incidence ϕinc).

Contrary to metal nano-particles, where the “cloud” of conduction electrons becomes polarised on resonance, the resonant modes of the teardrop originate from SPPs propagating in opposite directions around the periphery of the structure and interfering constructively at a set of discrete wavelengths (Fig. 3). Very narrow FWHM result because the resonances originate from wave (SPP) interference.

3. Analysis in water

The high Q of the teardrop suggests its suitability for biosensing. To examine this possibility we assume the same teardrop but with water [16

16. D. J. Segelstein, The Complex Refractive Index of Water, M.Sc. Thesis, University Of Missouri, Kansas City (1981).

] replacing vacuum (an aqueous solution is generally used as a carrier fluid for analyte [17

17. P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10(10), 105010 (2008). [CrossRef]

]). The scattering cross-section of the teardrop computed in this case is plotted as the thin blue curve in Fig. 2. The four resonances are red-shifted relative to vacuum. This is due to an increase in the effective index of the SPPs propagating on the teardrop commensurate with the increase in surrounding refractive index (from nd = 1 to ~1.30).

From the experimental perspective, a resonance and its FWHM could be interrogated by measuring the scattered intensity at a location far from the teardrop due to excitation by an incident beam. Thus, the radar cross-section is representative, and in 2D is given by [1

1. C. R. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

]:

σ2D=2πR|Escat(λ0)|2/|Einc(λ0)|2
(2)

The mono-static radar cross-section corresponds to the case where the transmitter and receiver are co-located. We assume co-location at y = 60 µm (R = 60 µm in Eq. (2)) and we compute the responses near the resonances on the thin blue curve of Fig. 2. The results are plotted in Fig. 4
Fig. 4 Mono-static radar cross-section (in µm) of the teardrop in water near the four resonances observed on the thin blue curve of Fig. 2.
, from which λr, FWHM and Q are determined, and listed in Table 2

Table 2. Radar Cross-Section Parameters of Resonant Modes; Au Teardrop in Water.

table-icon
View This Table
| View All Tables
.

The FWHM of the teardrop in water (Table 2) does not follow the mode order, as for the teardrop in vacuum (Table 1). In water, the FWHM of mode 1 is broader than the second and third modes. This is due to the absorption of water which increases rapidly with increasing wavelength in this range [16

16. D. J. Segelstein, The Complex Refractive Index of Water, M.Sc. Thesis, University Of Missouri, Kansas City (1981).

]. The narrowest FWHM (0.64 nm), obtained for mode 2, is much narrower than that of metal nano-structures such as ring-disk nano-cavities (FWHM > 130 nm) [9

9. F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano 3(3), 643–652 (2009). [CrossRef] [PubMed]

], nano-cubes (FWHM ~18 nm) [7

7. L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5(10), 2034–2038 (2005). [CrossRef] [PubMed]

], arrays of nano-rods (FWHM ~8.37 nm) [18

18. J. X. Cao, H. Liu, T. Li, S. M. Wang, Z. G. Dong, L. Li, C. Zhu, Y. Wang, and S. N. Zhu, “High-sensing properties of magnetic plasmon resonances in double- and triple-rod structures,” Appl. Phys. Lett. 97(7), 071905 (2010). [CrossRef]

], and nano-wires of rectangular to triangular cross-section (FWHM > 14 nm) [19

19. J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon resonances spectrum of silver nanowires,” Appl. Phys. B 73(4), 299–304 (2001). [CrossRef]

]. The largest Q (2019), also obtained for mode 2, is higher than in Ag-coated large diameter toroid micro-resonators (Q ~1000) [20

20. Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett. 105(15), 153902 (2010). [CrossRef] [PubMed]

] and in arrays of nano-rods (Q < 900) [18

18. J. X. Cao, H. Liu, T. Li, S. M. Wang, Z. G. Dong, L. Li, C. Zhu, Y. Wang, and S. N. Zhu, “High-sensing properties of magnetic plasmon resonances in double- and triple-rod structures,” Appl. Phys. Lett. 97(7), 071905 (2010). [CrossRef]

], but comparable to a micro-resonator based on a channel waveguide [21

21. S. Zamek, L. Feng, M. Khajavikhan, D. T. Tan, M. Ayache, and Y. Fainman, “Micro-resonator with metallic mirrors coupled to a bus waveguide,” Opt. Express 19(3), 2417–2425 (2011). [CrossRef] [PubMed]

], and 10 × smaller than long-range surface plasmon waveguide resonators [22

22. P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express 14(26), 13030–13042 (2006). [CrossRef] [PubMed]

].

The bulk sensitivity of the resonant modes ∂λr/∂nd was computed by perturbing the surrounding refractive index about the nominal value (i.e. nd ± 10−4) and approximating the partial derivative with a central difference formula [17

17. P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10(10), 105010 (2008). [CrossRef]

].The sensitivity of the four modes are listed in Table 2, and observed to decrease with mode order. The largest bulk sensitivity (1930 nm/RIU), obtained for mode 1, is much higher than that of isolated metal nano-particles, including nano-spheres and nano-branches [4

4. H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24(10), 5233–5237 (2008). [CrossRef] [PubMed]

], nano-rod chains [3

3. M. Piliarik, P. Kvasnička, N. Galler, J. R. Krenn, and J. Homola, “Local refractive index sensitivity of plasmonic nanoparticles,” Opt. Express 19(10), 9213–9220 (2011). [CrossRef] [PubMed]

], and ring-disk nano-cavities [9

9. F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano 3(3), 643–652 (2009). [CrossRef] [PubMed]

]. It also exceeds that of ring resonators in Si-on-insulator waveguides (SOI) [23

23. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007). [CrossRef] [PubMed]

].

Finally, we compute the figure of merit (FoM) of the four resonant modes via [7

7. L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5(10), 2034–2038 (2005). [CrossRef] [PubMed]

]:
FoM=(λr/nd)/FWHM
(3)
and list them in Table. The largest FoM (1702), observed for mode 2, greatly exceeds that of standalone metal nano-structures, such as nano-spheres (FoM ~0.6) [4

4. H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24(10), 5233–5237 (2008). [CrossRef] [PubMed]

], nano-bipyramids (FoM ~4.5) [4

4. H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24(10), 5233–5237 (2008). [CrossRef] [PubMed]

], and nano-cubes (FoM ~8 to 20) [11

11. S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: A route to increased-sensitivity localized Surface Plasmon resonance sensors revealed,” Nano Lett. 11, 1657–1663 (2011). [CrossRef] [PubMed]

]. It also greatly exceeds that of arrangements of metal nano-structures, such as clusters of nano-disks (FoM ~5.7) [24

24. J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010). [CrossRef] [PubMed]

], arrays of nano-rods (FoM ~2 to 90) [18

18. J. X. Cao, H. Liu, T. Li, S. M. Wang, Z. G. Dong, L. Li, C. Zhu, Y. Wang, and S. N. Zhu, “High-sensing properties of magnetic plasmon resonances in double- and triple-rod structures,” Appl. Phys. Lett. 97(7), 071905 (2010). [CrossRef]

], and aggregates of nano-spheres (FoM ~8 to 10) [10

10. N. A. Mirin, K. Bao, and P. Nordlander, “Fano resonances in plasmonic nanoparticle aggregates,” J. Phys. Chem. A 113(16), 4028–4034 (2009). [CrossRef] [PubMed]

]. Finally, it also exceeds the FoM of an SPP interferometer in SOI (FoM ~240) [25

25. K. Q. Le and P. Bienstman, “Enhanced sensitivity of silicon-on-insulator surface plasmon interferometer with additional silicon layer,” IEEE Photon. J. 3(3), 538–545 (2011). [CrossRef]

].

4. Summary and concluding remarks

We proposed a metal teardrop-shaped cylindrical resonator and demonstrated that it can find applications as a high Q resonator and as a high-performance biosensor element. Resonant modes involve SPPs circulating and interfering around the periphery of the structure, leading to narrow resonant line-widths. The resonant modes of a teardrop in water have a bulk sensitivity in the range of 538 to 1930 nm/RIU, a FWHM in the range of 0.64 to 1.9 nm, a Q in the range of 374 to 2019, and a FoM in the range of 282 to 1702. In vacuum, the smallest FWHM observed is 0.6 nm and the largest Q observed is 3400. These performance characteristics should be attainable in carefully fabricated structures having smooth sidewalls.

Acknowledgments

The High Performance Computational Virtual Laboratory (Canada) and the Research Institute for ICT (Iran) are gratefully acknowledged.

References and links

1.

C. R. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

2.

M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photon. Rev. 2(3), 136–159 (2008). [CrossRef]

3.

M. Piliarik, P. Kvasnička, N. Galler, J. R. Krenn, and J. Homola, “Local refractive index sensitivity of plasmonic nanoparticles,” Opt. Express 19(10), 9213–9220 (2011). [CrossRef] [PubMed]

4.

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24(10), 5233–5237 (2008). [CrossRef] [PubMed]

5.

N. Large, J. Aizpurua, V. K. Lin, S. L. Teo, R. Marty, S. Tripathy, and A. Mlayah, “Plasmonic properties of gold ring-disk nano-resonators: fine shape details matter,” Opt. Express 19(6), 5587–5595 (2011). [CrossRef] [PubMed]

6.

H. Y. She, L. W. Li, O. J. Martin, and J. R. Mosig, “Surface polaritons of small coated cylinders illuminated by normal incident TM and TE plane waves,” Opt. Express 16(2), 1007–1019 (2008). [CrossRef] [PubMed]

7.

L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5(10), 2034–2038 (2005). [CrossRef] [PubMed]

8.

E. Verhagen, L. K. Kuipers, and A. Polman, “Plasmonic nanofocusing in a dielectric wedge,” Nano Lett. 10(9), 3665–3669 (2010). [CrossRef] [PubMed]

9.

F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano 3(3), 643–652 (2009). [CrossRef] [PubMed]

10.

N. A. Mirin, K. Bao, and P. Nordlander, “Fano resonances in plasmonic nanoparticle aggregates,” J. Phys. Chem. A 113(16), 4028–4034 (2009). [CrossRef] [PubMed]

11.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: A route to increased-sensitivity localized Surface Plasmon resonance sensors revealed,” Nano Lett. 11, 1657–1663 (2011). [CrossRef] [PubMed]

12.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

13.

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B 70(12), 125113 (2004). [CrossRef]

14.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

15.

E. Marx, “Electromagnetic scattering from a dielectric wedge and the single hypersingular integral equation,” IEEE Trans. Antenn. Propag. 41(8), 1001–1008 (1993). [CrossRef]

16.

D. J. Segelstein, The Complex Refractive Index of Water, M.Sc. Thesis, University Of Missouri, Kansas City (1981).

17.

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10(10), 105010 (2008). [CrossRef]

18.

J. X. Cao, H. Liu, T. Li, S. M. Wang, Z. G. Dong, L. Li, C. Zhu, Y. Wang, and S. N. Zhu, “High-sensing properties of magnetic plasmon resonances in double- and triple-rod structures,” Appl. Phys. Lett. 97(7), 071905 (2010). [CrossRef]

19.

J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon resonances spectrum of silver nanowires,” Appl. Phys. B 73(4), 299–304 (2001). [CrossRef]

20.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett. 105(15), 153902 (2010). [CrossRef] [PubMed]

21.

S. Zamek, L. Feng, M. Khajavikhan, D. T. Tan, M. Ayache, and Y. Fainman, “Micro-resonator with metallic mirrors coupled to a bus waveguide,” Opt. Express 19(3), 2417–2425 (2011). [CrossRef] [PubMed]

22.

P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express 14(26), 13030–13042 (2006). [CrossRef] [PubMed]

23.

K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007). [CrossRef] [PubMed]

24.

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010). [CrossRef] [PubMed]

25.

K. Q. Le and P. Bienstman, “Enhanced sensitivity of silicon-on-insulator surface plasmon interferometer with additional silicon layer,” IEEE Photon. J. 3(3), 538–545 (2011). [CrossRef]

OCIS Codes
(230.5750) Optical devices : Resonators
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Optics at Surfaces

History
Original Manuscript: January 23, 2012
Revised Manuscript: February 14, 2012
Manuscript Accepted: February 28, 2012
Published: March 5, 2012

Citation
Majid Rasouli Disfani, Mohammad Sadegh Abrishamian, and Pierre Berini, "Teardrop-shaped surface-plasmon resonators," Opt. Express 20, 6472-6477 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-6-6472


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References

  1. C. R. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  2. M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photon. Rev.2(3), 136–159 (2008). [CrossRef]
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